Emergence of Collective Organizational Phenomena in Manybody Systems

微观力控制的量子世界和支配我们日常生活的宏观世界之间的联系还没有得到很好的理解。宏观系统表现出普遍的行为，不能敏感地依赖于微观细节，但被认为是服从于强大的和普遍的组织原则。在物理学的许多分支中，包括早期宇宙的夸克-胶子等离子体，高温超导性和实验室中的超冷费米气体，在各种感兴趣的系统中都可以看到普遍行为。在这个项目中，私家侦探将调查这些产生宏观系统集体行为的强大力量的出现。该计划是对系统大小的函数性质进行系统研究，重点研究量子力学和经典力学融合的中间区域，称为介观区域。本科生和研究生都将充分参与这项研究，包括通过论文和演讲交流结果。这项研究的科学目标是阐明这种新兴的普遍行为背后的驱动力，并提出在实验室中观察和控制这种行为的新方法。在过去的十年里，原子物理学界已经利用冷却和捕获技术来创建和控制具有普遍特性的有限尺寸的超冷气体系统。这项工作将集中在费米气体上，并利用微扰方法同时对所有系统大小产生精确的一阶结果。通过研究趋势作为系统大小的函数，例如最近在实验室测量的激励频率和热力学量，我们的目标是揭示新兴集体行为的特征，以便了解这种基本转变的动力学。

The connection between the quantum world controlled by microscopic forces and the macroscopic world that dominates our everyday lives is not well understood. Macroscopic systems exhibit universal behavior that cannot depend sensitively on microscopic details, but is believed to be subject to powerful and general principles of organization. Universal behavior is seen in a variety of systems of interest across many branches of physics including the quark-gluon plasma of the early universe, high temperature superconductivity and ultracold Fermi gases in the laboratory. In this project, the P.I. will investigate the emergence of these powerful forces that give rise to the collective behavior of macroscopic systems. The plan is to perform a systematic study of properties as a function of system size, focusing on an intermediate regime called the mesoscopic region where quantum mechanics and classical mechanics merge. Both undergraduate and graduate students will participate fully in this research, including communicating the results through papers and talks.The scientific goal of this study is to elucidate the driving forces behind this emerging universal behavior and to propose new ways to observe and control this behavior in the laboratory. In the last decade, the atomic physics community has taken advantage of cooling and trapping techniques to create and control finite-size systems of ultracold gases that exhibit universal properties. This work will focus on Fermi gases and utilize a perturbation method that yields exact first-order results for all system sizes simultaneously. By studying trends as a function of system size for properties such as excitation frequencies and thermodynamic quantities recently measured in the laboratory, the goal is to uncover signatures of emerging collective behavior in order to understand the dynamics of this fundamental transition.